Systems and methods for high-magnification high-resolution photography using a small imaging system

ABSTRACT

Imaging systems and methods are provided for taking high-magnification photographs confined to a small physical volume. In some embodiments the system is composed of at least one lens, one or more partially reflective elements, and a sensor. The partial reflectors reflect a portion of the light back and forth between them to allow a long path length for a portion of the light from the lens to the sensor which enables a high magnification.

TECHNICAL FIELD

This application relates to imaging, and more particularly to imagecapture, and in particular but not exclusively, relates to cameras andphone cameras. This application also relates to a camera built into asmartphone, a laptop, a tablet, or any other apparatus.

BACKGROUND

Smartphone and mobile device have become compact and thin, which haslimited their optical magnification. A larger optical magnification isnecessary to take high-quality photographs of objects that are far awayfrom the camera or user. Typically, large optical magnification requiresa long distance between the lens and the camera sensor. Cell phones,smart phones, tablets and other mobile devices are thin, which limitsthe distance between the lens and the camera sensor which restricts theachievable magnification. As the dimensions of smartphones and mobiledevices shrink, the camera dimensions become more and more a key factorthat limits image quality.

More specifically, FIG. 2 illustrates why a long distance from lens tosensor has been required to achieve high-magnification, high-resolutionimage capture. The lens (201) collects light from the object (101) whichis a distance (d) away from the lens, and forms an image at a distance(f) away from the lens on the camera sensor (501). The magnification ofsuch a system can be stated as M=f/d. Thus, to get a largermagnification requires a longer distance between the lens and sensor.FIG. 2A shows the case where f=fA, where fA is a distance. In this casethe image (810) formed on the sensor array is large (of size hA), andthe image is well resolved on the sensor elements (sensor pixels).

In smartphone or cell phone cameras, the distance from lens to sensorcannot be made larger without increasing the thickness of the phone.Current phones use a distance f of only 4-6 mm, which is why the phoneshave poor magnification. Referring now to FIG. 2B, the distance betweenthe lens and sensor is f=fB, where fB is a shorter distance because thecell phone thickness restricts the distance between the lens and sensor.Hence the resulting image (820) on the sensor array is small (of sizehB), has only overlaps of a few sensor elements, and is therefore poorlyresolved. This poor resolution cannot be cured by pinch zooming on thephone, since all that does is show the user the image that has beencollected on the small number of sensor elements, the image resolutionremains poor. With the short focal length in typical phones or tablets,high-magnification high-resolution information from far away objects islost and cannot be recovered using current technology.

FIG. 3 further illustrates how the thickness (length or depth) of theimaging device impacts photography of far-away or long distance objects.If the image is taken with a long focal length lens, such as the lens ona DSLR camera shown in FIG. 3 (A2), and correspondingly the sensor is along distance from the lens, then a far-away object will be imaged ontomany pixels and will therefore show a high degree of detail shown inFIG. 3 (A1). But if the image is taken with a small focal length lens ina cell phone shown in FIG. 3 (B2), and correspondingly the sensor isclose to the lens, then the object will only be imaged on a small numberof pixels and will therefore look blurry and pixelated FIG. 3 (B1).

Thus, there is a need for improved imaging systems and methods tocapture images in a thin device such as a cell phone, tablet, or othermobile device. It is to these needs among others, that this applicationis directed.

SUMMARY

This application includes methods and systems that produce anhigh-magnification image of further away objects from the imaging device(e.g., a cell phone camera). One embodiment includes a lens, two partialreflectors, and a sensor, which may be an imaging camera sensor or othertype of light sensor. In specific examples, the distance between thelens and sensor is less than 20 mm. Light is focused by the lens, andundergoes multiple partial reflections between two partial reflectors.Each partial reflection results in a longer optical path length untilthe light reaches the sensor. The distance between the two partialreflectors can be selected such that a specific number of round tripsbetween the partial reflectors forms a focused image at the sensor,while other lesser or greater number of round trips form a less focusedimage or desired focus.

Another aspect includes a signal processing unit that processes theoutput of the imaging sensor. The signal processing unit may process thesensor information in order to generate a focused image from the rawsensor data, composed of the focused image on the sensor plus the out offocus images on the sensor. The signal processing unit can be composedof a digital signal processor such as a computer, microprocessor, orfield programmable gate array, or by any other means. In otherimplementations it may be composed of an analog signal processor. Thesignal processing unit may be an optical signal processor that directlyperforms signal processing on the optical field. In theseimplementations the order of the signal processing unit and sensor maybe interchanged such that the optical signal processor first processesthe light, and the sensor then measures it.

Another aspect includes methods and systems that include additionallenses placed before, after, or in-between the two partial reflectors.These lenses can serve a number of functions including correction foraberrations. The lens can be a glass lens, molded plastic lens, zoneplate, fresnel lens, or any other optical element that achieves focusingof light. The lens could be replaced by a fresnel lens, to achieve aneven thinner form factor due to the reduction in thickness of thefresnel lens.

Another aspect includes methods and systems in which one or more of thepartial reflectors are replaced with a one-way mirror. A one-way mirrorallows light to transmit when entering one end of the mirror, andreflect when incident from the other end. A one-way mirror may be usedto reduce the amount of light that is lost out of the device and doesnot reach the sensor.

Another aspect includes methods and system in which some of the partialreflectors and lenses are replaced by partially-reflecting curvedmirrors. A partially-reflecting curved mirror serves a combined role ofa partial reflector and a focusing element, thus reducing the overallnumber of elements and enabling a thinner overall device. Because lightreflects multiple times off of the partial reflector, a curved partialreflector with a longer radius of curvature may be used enabling both amore compact device, and also reducing aberrations. In other examplesone of the curved mirrors may be replaced by a one-way curved mirror,which allows light to fully reflect from one direction and fullytransmit from another direction.

Another aspect includes methods and systems to perform imaging with adevice or cameras whose physical length is shorter than the distancerequired by the light to travel from the lens to the imaging plane. Inan exemplary embodiment, the methods and systems can include a lens,two-partial reflectors, a sensor, and a signal processor, whereby lightundergoes multiple partial reflections between the two partialreflectors, thereby traveling a longer distance than the physicaldistance between the lens and sensor. The sensor then sums the partialreflections, and the signal processing unit post-processes the signal.In some implementations the focal length of the lens and the distancebetween the partial reflectors may be chosen such that after a desirednumber of round-trip partial reflections, the lens forms a focused imageon the sensor. In such methods the signal processing unit may then takethe signal and reject the out-of-focus or less than focused componentsof the signal originating from the undesired number of round trips, andsubstantially retain only the signal originating from the desired numberof trips.

Another aspect include methods and system in which one or more partiallyreflective mirrors can be replaced by one or more one-way mirrors, toreduce the round-trip losses of light. Other implementations may includeaddition lenses before, in-between, and/or after the partial reflectorsto perform aberration correction or implement high-magnification imagingwith an increased light travel length between the lenses due to multiplepasses. In other implementations of the method one or more of the lensesand/or partial reflectors may be replaced by partially-reflective curvedmirrors. These partially-reflective curved mirrors may be used toachieve focusing with a longer radius of curvature, thereby reducing theoverall device size.

Another aspect includes an imaging system comprising a lens, a firstpartial reflector, a second partial reflector, and a sensor, in whichlight transmits through the lens, undergoes multiple partial reflectionsbetween the partial reflectors, and is subsequently imaged by thecamera. The lens and the second partial reflector are a distance lessthan 30 mm, less than 18 mm, less than 10 mm or less than 8 mm. A signalprocessing unit can process the signal by the camera to form an improvedimage. The focal length of the lens allows light from the object(s) orscene to produces a focused image on the time-integrating sensor whenundergoing a desired number of round trips between the partialreflectors.

Another aspect includes an imaging system comprising a lens, a one waymirror, a partial reflector, and a sensor, wherein light transmitsthrough the lens, undergoes multiple partial reflections between thepartial reflectors, and is subsequently imaged by the camera, whereinthe lens and the second partial reflector are a distance less than 30mm, wherein the one-way mirror fully transmits light that has passedthrough the lens, and fully reflects light that has been reflected fromthe partial reflector. The lens can be a glass lens, a molded plasticlens, a zone plate, or a fresnal lens. The plurality of partialreflectors can have an average optical reflectance of at least 5% in apre-determined plurality of wavelengths

Another aspect includes an imaging system having additional lenses thatare placed before, after, or in-between the first partial reflector orthe second partial reflector.

Another aspect includes an imaging system having additional lenses thatare placed before, after, and/or in-between the partial reflectors.

Another aspect includes partial reflectors in which a pre-determinedplurality of wavelengths are one or more continuous wavelength ranges.

Another aspect includes an imaging system in which at least one lens isreplaced by at least one partially reflective curved mirror.

Another aspect includes an imaging system in which the lens has adiameter and the diameter is larger than the thickness of the system.

Another aspect includes an imaging system in which some or all of thelenses or flat partially-reflective elements are replaced by partiallyreflective curved mirrors.

A method to optically image an object or scene using a lens, at leasttwo partial reflectors, a time-integrating sensor, and a signalprocessing unit such that incoming light undergoes multiple partialreflections before hitting the sensor, enabling the signal processingunit to generate an image a lens whose back focal length is longer thanthe physical distance between the lens and sensor. One or more of thepartially reflective elements can be replaced by a one-way mirror.Additional lenses can placed before, after, and/or in-between thepartial reflectors in order to correct for imaging aberrations.Additional lenses can be placed before, after, and/or in-between thepartial reflectors in order to correct for imaging aberrations. The lenscan be replaced by at least one partially reflective curved mirror. Thelens can be replaced by at least one partially reflective curved mirror.Some or all of the lenses can be replaced by partially reflective curvedmirrors.

Another aspect includes a camera or other smart device or the likehaving a lens, a first partial reflector, a second partial reflector,and a sensor, wherein light transmits through the lens, undergoesmultiple partial reflections between the partial reflectors, and issubsequently imaged by the camera, wherein the lens and the secondpartial reflector are a distance less than 30 mm.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an embodiment having a lens, two partial reflectors,and an imaging sensor;

FIG. 2 illustrates the general relationship of magnification to focallength in prior art devices;

FIG. 3 provides images of a monument or object taken with prior art,with a long focal length camera and a short focal length smartphone;

FIG. 4 illustrates an embodiment of a cellphone containing a lens, twopartial reflectors, and an imaging sensor;

FIG. 5 illustrates an exemplary embodiment having traditional imagingelements;

FIG. 6A illustrates an exemplary reconstruction of the path of thelight, and how an in-focus image is formed on the sensor plane;

FIG. 6B illustrates the partial reflection of the light in a partialreflector;

FIG. 7 illustrates images after none, one, two, and three round-trippartial reflections, and also shows the resulting total image;

FIG. 8 is a flow diagram of an exemplary method for capturing ahigh-resolution image at a distance;

FIG. 9 illustrates an embodiment having a lens, a one-way mirror, apartial reflector, and an imaging sensor;

FIG. 10 illustrates an embodiment with two inward facingpartially-reflective curved mirrors and an imaging sensor;

FIG. 11 illustrates another embodiment in which a phone has a lens witha larger diameter;

FIG. 12 shows a flow diagram of an exemplary method for imageacquisition and signal processing;

FIG. 13 shows experimental images a Snellen eye chart taken though anIphone 7, and Iphone 11 with a 2× zoom, and an example of the embodimentshown in FIG. 1 ;

DETAILED DESCRIPTION

Specific embodiments include imaging systems or cameras and methods thatinclude a lens, a first partial reflector, a second partial reflector,and a sensor; and may include additional elements (e.g., to allow forhigher contrast, reduced chromatic aberrations, filtering light, and thelike). Specific embodiments can provide images that are of highmagnification, have high contrast, and have reduced imaging aberrations.Further, the imaging system or camera may be implemented in a smallvolume while still capturing focused, high-magnification,high-resolution images, making embodiments of the camera suitable foruse in small and/or mobile multipurpose devices such as cell phones,smartphones, pad or tablet computing devices, laptops, netbooks,notebooks, subnotebooks, and ultrabook computers, and so on. Aspects ofthe camera (e.g., the lens system and imaging sensor or photosensor) maybe scaled up or down to provide cameras with larger or smaller packagesizes. Embodiments of the camera system can be implemented asstand-alone digital cameras. Embodiments of the camera system can beadapted for use in video camera applications.

One embodiment includes a system comprising a lens, a first partialreflector, a second partial reflector, and a sensor; and these elementscan be within the compact thickness, depth or length of a small imagingsystem. The light transmits through the lens, undergoes multiple partialreflections between the partial reflectors, and is subsequently imagedby the sensor. A signal processing unit processes the signal from theimaging sensor to form an improved image. The focal length of the lenscan be selected such that light from the object(s) or scene produces afocused image on the sensor when undergoing a desired number ofround-trip reflections between the partial reflectors.

FIG. 1 illustrates an exemplary embodiment. The exemplary system has alens (201), two partial reflectors (301 and 302), and a sensor (501).The number of elements can be increased (e.g. additional lenses orpartially reflective mirrors), and may include concave lens or lensesinstead of or in addition to a convex lens, curved partially-reflectivemirrors instead of flat ones, etc. The element can be arranged on anoptical axis to transmit, focus, and reflect light from the object toultimately the sensor. These elements can be with the compact depth of acamera system, which may be less than 30 mm, 20 mm, 18 mm, 16 mm, 14 mm,12 mm, 10 mm, 8 mm, 6 mm, 4 mm, or the like.

The distance from the lens to the second partial reflector can be varieddepending on the specific imaging system or smartphone. In someembodiments, the distance between the lens to the second partialreflector may be less than 20 mm. In some embodiments, the distancebetween the lens to the second partial reflector may be less than 15 mm.In some embodiments, the distance between the lens to the second partialreflector may be less than 10 mm. In some embodiments, the distancebetween the lens to the second partial reflector may be less than 8 mm.In some embodiments, the distance between the lens to the second partialreflector may be less than 6 mm. The focal length and/or other lenssystem parameters may be scaled or adjusted to meet specifications ofoptical, imaging, and/or packaging constraints for other camera systemapplications.

Referring back to FIGS. 2A and 3 , the embodiment shown in FIG. 1addresses or reduces the need for a long focal length to takehigh-magnification images. FIG. 2A show a prior-art case where the focallength f=fA is long, and a large (high magnification) image is formed onthe imaging sensor (A). The image (810) overlaps many sensor elements onthe imaging sensor, and therefore is accurately resolved. In contrast,FIG. 2B shows a case where the focal length f=fB is small and a small(low magnification) image is formed on the imaging sensor. This image(820) overlaps only a few sensor elements on the imaging sensor, and istherefore not well resolved. The elements shown in FIG. 2 are the object(101) of dimension h, rays (611 and 612) emanating from the tips of theobject, a lens (201) that is a distance d away from the object, a longcamera (110, 510) with a long focal length of fA, and a thin cell phonecamera (120, 520) with a short focal length of fB, and the resultinghigh-magnification highly-resolved image (810) of large size hA formedby the long camera on the imaging sensor (501), versus thelow-magnification poorly-resolved image (820) of small size hB formed bythe cell phone camera on the imaging sensor (501).

FIG. 4 is a cross-sectional illustration of an example compactsmartphone 700 including a compact narrow imaging system that includeslens 201, partial reflectors 301, 302, image sensor 501, andprocesser/PCB board 701, that is connected to the sensor by connection702. The embodiments disclosed herein can enable long focal lengthphotographs using a compact imaging system. The disclosed imaging systemthat can fit inside the width and thickness of a smartphone 700. Thesmartphone 700 allows for focused, high-magnification imaging and/orphotography of an object, objects, or scene using an imaging systemcontained in a compact volume. The compact volume, for example, issufficiently small and can have a form factor (is thin enough) to beused inside a cell phone, a smart phone, a laptop, or a tablet. Theimaging system allow a portion of light into the volume between them andback out, and also to allow reflections of a portion of the lightback-and-forth between them (between the partial reflectors). Theimaging sensor 501 can then detect the portion of the light that exitsthe volume between the partial reflectors 301, 302. In an exemplarysetting, the portion of the light that has been partially-reflectedbetween the partial reflectors a desired number of times and thenreaches the sensor, that light may produce a focused image of theobject, objects, or scene on the sensor.

FIG. 5 is an illustration of a specific example of a compact camera 700including the imaging system that includes an aperture 741, shutter 731,a lens 201, two partial reflectors 301, 302, a filter 721, a photosensor or image sensor 501, and a PCB board 711. FIG. 5 illustratesadditional elements that may be included in an imaging system and thatis included inside a smartphone, a laptop, a tablet, or other device. Inaddition to a lens and two partial reflectors and an imaging sensor,these may include an aperture, a shutter, a filter or filters, a PCBboard, along with other components that may be included as part of animaging system or a camera.

FIG. 6A shows the path of light in an exemplary embodiment. It showsrays of light 600 and 601 from a point 102 on an object 101 pass throughthe lens 201. A fraction of the light 631 transmits through the firstpartial reflector 301. A fraction of this transmitted light thenundergoes a desired number of partial reflections (e.g., 2 round-trippartial reflections, rays 631, 641, 651, 661, 671) between the twopartial reflectors 301, 302. A fraction of this light (label 672) thentransmits through the second partial reflector and reaches the sensor(label 501). In an exemplary case, the fraction of light from saidobject undergoes the desired number of one or more partial reflections,and produces a focused image of the object at the imaging sensor (hereshown by rays 600 and 672 meeting at the point 602 on the sensor, whichforms an in-focus image of point 102 of the object). In one embodiment,the partial reflector may have an average optical reflectance of atleast 5% in the desired or pre-determined plurality of wavelengths andmay have an average optical transmittance of at least 95% in the desiredor pre-determined plurality of wavelengths. In one embodiment, thepartial reflector may have an average optical reflectance of at least10% in the desired or pre-determined plurality of wavelengths and mayhave an average optical transmittance of at least 90% in the desired orpre-determined plurality of wavelengths. In one embodiment, the partialreflector may have an average optical reflectance of at least 15% in thedesired or pre-determined plurality of wavelengths and may have anaverage optical transmittance of at least 85% in the desired orpre-determined plurality of wavelengths. In one embodiment, the partialreflector may have an average optical reflectance of at least 25% in thedesired or pre-determined plurality of wavelengths and may have anaverage optical transmittance of at least 75% in the desired orpre-determined plurality of wavelengths. The desired reflectance dependson how many partial reflections the light must undergo before forming afocused image. For small number of partial reflections, the reflectancecan be set to be lower so that a larger fraction of the incident lighttransmits through the first partial reflector when existing the lens, ortransmits through the second partial reflector before reaching thesensor. For larger number or partial reflections, the reflectance can beincreased to reduce the round-trip loss. This reduction in round-triploss comes at the expense of having less light transmit through thefirst partial reflector after the lens, or the second partial reflectorprior to reaching the sensor. The actual reflectance used can beselected to balance off these competing losses with the optimal valuedepending on the respective application. In some embodiments, thedesired or pre-determined plurality of wavelengths may be a singlecontinuous range of wavelengths (e.g., a visible range of 400 nm to 700nm) or it may be a plurality of continuous ranges of wavelengths. Insome embodiments, the range of wavelengths are in the ultraviolet range.

As an exemplary case for optimally selecting the reflectance percentageR, the focused image occurs after K round trips. The transmittanceT=1−R, and I as the intensity of the light hitting a pixel on the cameraare used here. The component of the light with the desired number ofround trips has a relative intensity ofI _(d) =IT ² R ^(2K)while the intensity from all of the undesired components has a relativeintensity of

$I_{nd} = {{IT}^{2}\left( {\frac{1}{1 - R^{2K}} - R^{2K}} \right)}$

Here is disclosed selecting the reflectance percentage R to maximize thesignal to background ratio

${SBR} = {\frac{I_{d}}{I_{nd}}.}$In particular, in this exemplary instance the SBR achieves an optimalmaximal value when

$R = {\sqrt{\frac{K}{1 + K}}.}$This exemplary case shows how the reflectance R can be optimallyselected given a desired performance metric, in this case the SBR. Aperson knowledgeable in the arts of optics and optimization willrecognize that other metrics may also be used, and their use isanticipated and disclosed and thus the above example should not beconsidered limiting to the scope of the invention.

The thickness or length of the disclosed system can be stated as thedistance from the start of the lens 201 to the sensor plane. Referringback to FIG. 1 , in an exemplary case, this length is composed of thelength L1 from the start of lens 201 to the start of the first partialreflector 301, L2 is the distance from the start of the first partialreflector 301 to the end of the second partial reflector 302, and L3 isthe distance from the end of the second partial reflector 302 to thestart of the imaging sensor 501. Hence the length of the exemplarysystem of FIG. 1 is approximately the sum of these 3 distances, plus asmall amount due to the thickness of the imaging sensor and any backingmaterials behind the sensor.

FIG. 6A and FIG. 6B show the elements of an embodiment and the path ofthe light is described in further detail. In FIG. 6A, other elements ofthe light path that will be readily understood by someone knowledgeablein the art of optics are not shown only for reasons of simplifiedillustration. The exemplary point 102 on an exemplary object 101 can beimaged or photographed, and two example rays of light 600, 601 emanatefrom that point. Shown is the top angled emanating ray (label 601), thedisclosed path of this ray and the elements that enable that light pathand hence enable high-magnification imaging in a small volume. Incontrast, light ray 600 is along the centerline of the system and is notat an angle, and so partial-reflections of this ray will overlay theunreflected ray 600 in the figure, and thus these partial reflectionsare not marked in the figure. As noted, the disclosed path of the lightis described primarily for the top angled ray (ray 601). Thetransmissions and partial reflections of a bottom angled ray (the mirrorimage of 601 along the centerline, not shown) are equivalent, and arenot shown only for reasons of convenience to avoid cluttering thefigure. All other rays that are at angles in between the top and bottomof the lens, those rays will behave similarly, and will all alsosubstantially emanate from point 102 and reach point 602 in-focus aftertwo round trip partial reflections. It is understood that thephysics/optics of these rays follows the same physics/optics asexemplary rays 600, 672.

In FIG. 6 , the embodiment is shown with two round-trip partialreflections to generate an in-focus image at the sensor. A minimum oftwo round trip reflections can be one embodiment, and is not limiting, alesser or greater number of intended partial reflections is alsodisclosed. In FIG. 6A, light ray 601 is transmitted through the lens201, is bent by the lens, and comes out as ray 621. Ray 621 hits thefirst partial reflector (label 301) and a portion of the light isreflected back (ray 622) while another portion of that light istransmitted through the partial reflector because that reflector ispartial and thus lets through a portion of the light. A portion of ray621 thus enters the volume between the two partial reflectors (ray 631).The portion of the light labelled as ray 631 continues on and hits thesecond partial reflector (label 302). Now a portion of that light istransmitted (ray 632) out of the volume between the partial reflectors,but another portion is reflected (ray 641) back into the volume betweenthe partial reflectors. Ray 631 (forward) and ray 641 (backward)comprise the first round-trip of the light between the two partialreflectors.

To in more detail illustrate the function of the partial reflectorsspecifically, FIG. 6B shows said light ray 631 hitting the secondpartial reflector (or the first partial reflector functions equally),whereby a portion of the light is reflected (e.g. a percent R of thelight is reflected back, ray 641), and a portion of the light istransmitted through (e.g. a percent T of the light is transmitted, ray632). For illustration and example purposes only, if R=60% and sixtypercent of the light is reflected, then (ignoring other effects such aslight scattering), substantially a portion of the light T=(1−R)=40% orforty percent of the light may be transmitted.

Now referring back to FIG. 6A, the path of light in this exemplarysystem continues as follows. The portion of light ray 641 that isreflected by the first partial-reflector, that ray 651 continues backinto the volume between the two partial reflectors and hits the secondpartial-reflector again. Now a portion of ray 651 is transmitted out(ray 652) and a portion is reflected back again into the volume betweenthe two partial reflectors (ray 661). In turn, ray 661 hits the firstpartial-reflector again, a portion of it is transmitted out (ray 662)and a portion is reflected back (ray 671). Ray 651 (forward) and ray 661(backward) comprise the second round-trip of the light between the twopartial reflectors.

Ray 671 hits the second partial-reflector again and a portion of it isreflected back, but the remaining portion is transmitted out (ray 672).This ray 672 hits the imaging sensor at point 602. Thus, along thepreferred exemplary pathway disclosed above, a portion of the light frompoint 102 on object 101 traverses the lens 201, enters the volumebetween the two partial reflectors (301 and 302), traverses tworound-trip reflections (ray 621 to 631 to 641 to 651 to 661 to 671), andthen exits the volume between the two partial-reflectors through thesecond partial-reflector (ray 672) to hit the sensor 501 at location602. In this exemplary setting, the other ray 600 also from point 102 onobject 101, a portion of that ray also reaches the imaging sensor 501 atthe same location 602. Thus the image formed on the sensor after tworound-trip reflections between the partial reflectors produces a focusedimage of point 102 of object 101 on the imaging sensor 501. The essenceof the invention is that this in-focus image is produced by a light-paththat is substantially longer than the thickness of the imaging system,thus enabling a long focal length in a small and compact imaging system.The effect can be further amplified by selecting a lens with a focallength that matches the light path for 3, 4, 5, 6, . . . intendedpartial reflections, thus even further increasing the focal length foran imaging system still of the same small size.

The disclosed path of the portion of the light that undergoes tworound-trip reflections between the partial reflectors, and which saidportion arrives in focus at the imaging sensor, that light traverses agreater distance than the length (thickness) of the exemplary imagingsystem disclosed in FIG. 1 . Specifically, the light traverses thedistance between the partial reflectors five (5) times, once to crossthe distance between them, and twice more for each round-trip partialreflection. Thus in an exemplary instance, for K desired round trips,the distance light travels after undergoing the desired number of roundtrips is given by the formulaf=L ₁+(1+2K)L ₂ +L ₃   [Eqn 1.]

As is evident from the formula, and from FIGS. 1 and 6A, the distance fis substantially greater than the length (thickness) of the illustratedexemplary system. The length (thickness) of the imaging system is justL=L₁+L₂+L₃, but the length traveled by the light is greater than L dueto the amplification by multiplication factor (1+2K) of L₂ from the Kround-trip partial reflections. Thus the distance f is longer than thelength of the disclosed imaging system, because the distance between thetwo partial reflectors is quintuple (5×) counted (once for the firstpass of light, and twice more for the two round-trip reflections).Accordingly, the magnification achieved by this imaging system is M=f/dwith f according to equation (1), and this said magnification is muchgreater (larger) than would be achieved by prior-art systems of the samesize. If the number of desired partial reflections K is selected to belarger than two, for example if it is selected to be K=3 or 4 or 5 or 6,etc., then the magnification achieved by such an imaging system will beeven larger, while the size of said imaging system will remain unchangedat L=L₁+L₂+L₃.

In exemplary embodiments, e.g., FIG. 1 and FIG. 6A, the intended numberof round-trip partial reflections is two (K=2) and the portion of thelight that arrives from the object to the sensor after two round-trippartial reflections is in-focus at the imaging sensor. The images of theobject formed by portions of the light that arrive at the imaging sensorwith less than K reflections (e.g. after no or one round-trip partialreflection) or that arrive at the imaging sensor with more than Kreflections (e.g. after three or more round-trip partial reflections),those images will be out of focus.

FIG. 7 illustrates images of an object obtained after zero, one, two,and three round-trip partial reflections, along with their sum that iscollected on the image sensor. Here the lens focal length has beenselected to match light path-length for two round-trip partialreflections, hence the third image (panel C) is in-focus, while theother partial reflections are out-of-focus. FIG. 7 shows in furtherdetail how the current invention functions to provide high-magnificationimages by exploiting partial-reflections. A building was photographed ata long distance (2 miles). FIG. 7 shows a reconstruction of the imageformed on the imaging sensor after zero, one, two, and three round-tripreflections. As previously, the intended number of partial reflectionsis two (K=2), meaning that the lens focal length has been chosen to beconsistent with equation (1) for K=2. Panel A shows the image that isformed by the portion of the light that arrives at the sensor with nopartial reflections (k=0), for the exemplary embodiment of FIG. 1 andFIG. 6A, this image is out of focus. Panel B shows the image after oneround-trip partial reflection (k=1), this image is also out of focus.Panel C shows the image after two round-trip partial reflections(k=K=2), this image is in focus. Panel D shows the image after threeround-trip partial reflections (k=3), this image is again out of focus.The total image formed at the location of the imaging sensor is the sumof all images for k=0, 1, 2, 3, 4, etc. This resulting total image isshown in Panel E. Since only one of the sub-images that makes up thetotal image, the sub-image for k=2=K partial reflections, is in focus,this is the image component that is most apparent in the total imageformed. To further improve the quality of the total image, theout-of-focus sub-image components for the number of partial-reflectionsthat do not match the desired number of partial-reflections (for k≢K,i.e. for k=0, 1, 3 and 4, 5, . . . ), the effect of these out-of-focussub-images can be removed by imaging algorithms disclosed and describedherein.

In operation and use and as shown in FIG. 8 , an exemplary method forsignal processing, to substantially extract the in-focus image after theintended number of round-trip partial reflections. Disclosed is the pathof light through the imaging system. Specifically, in an embodiment,light enters through the lens. Part of the light gets reflected anintended number of times between partial reflectors. A portion of thatlight exits the volume between the partial reflectors and reaches animaging sensor. The sensor converts the light to electrical signals, andthose go to a signal processor. The signal processor generates a highquality image, for example by removing out-of-focus components from theimage, as disclosed herein.

In another embodiment (e.g., FIG. 9 ), a first partial reflector can bereplaced with a one-way mirror (401) that fully transmits light that haspassed through the lens, and fully reflects light that has beenreflected from the second partial reflector. A partial reflectorreflects a fraction R of the light and transmits a fraction T regardlessof whether the light is incident from the left or the right. Incontrast, a one-way mirror (element 401 in FIG. 9 ), fully transmitsincident from one direction (e.g. from the left), and fully reflectslight incident from the other direction (e.g. from the right). Replacingone or more of the partial reflectors with one-way mirror(s) may conferadvantages of reducing the amount of light that is lost out of thedevice. Labels in FIG. 9 are as previously for repeated elements,specifically: object 101, point on object 102, light rays 600 and 601emanating from that point, focusing lens 201, the first partialreflector has been replaced by the one-way mirror 401, and 302 is theremaining partial reflector, there is an imaging sensor 501, and point102 is focused to point 602 on the sensor after the intended tworound-trip partial reflections. The focal length of the system isf=L₁+5L₂+L₃, as per equation (1), and due to the partial reflectionsthat is substantially longer than the thickness of the deviceL=L₁+L₂+L₃.

A person knowledgeable in the art of optics will recognize that thereare many different types of lenses. These lenses may serve a number offunctions including correction for aberrations. The lens or lenses usedcould be one of the following, or a combination of these: a glass lens,molded plastic lens, zone plate, Fresnel lens, or any other opticalelement that achieves focusing of light. For example, a lens or lensescould be replaced by a Fresnel lens, to achieve an even thinner formfactor due to the reduced thickness of a Fresnel lens compared to aconventional lens.

FIG. 10 shows another embodiment in which a lens and two partialreflectors may be replaced with partially reflecting curved mirrors.Curved mirrors can have the same functionality as lenses by focusinglight rays (now by reflection instead of by transmission), but canconfer advantages of no or less chromatic aberrations. This arrangementfor partial reflections can increase the effective path of light and toincrease focal distance by the use of partially-reflecting curvedmirrors, which may be used instead of or in addition to a lens or lensesand flat partial reflectors. Referring to FIG. 10 , the exemplary deviceis composed of a first partially reflecting concave curved mirror (311),a second partially reflecting concave curved mirror arranged in theopposite direction (312), and an imaging sensor (501). Other elements inthe figure include an object with an exemplary point, two emanating rays(600 and 601), and their focus at point 602 on the imaging sensor afterone intended round-trip partial reflection. As illustrated by thisexample, different numbers of intended partial reflections areanticipated and disclosed. Previously, in FIG. 6 ., two intendedround-trip partial reflections were shown; here in FIG. 10 one intendedround-trip reflection is shown, and the curvature of thepartially-reflecting mirrors would be selected so that the focal lengthmatches the light path length for one intended partial reflection. Adifferent curvature could be selected for two, three, four or moreintended partial-reflections, and such a selection is anticipated anddisclosed.

It is understood that the number of elements may increase (e.g.additional lenses or mirrors), their form may change (e.g. one of thepartial reflectors may be flat instead of curved), or additionalelements may be placed in the system. Adding elements may be beneficialfor further improving system performance, for example to increasecontrast, reduce aberrations, reduce distortion, etc.

FIG. 11 shows smartphone 700 with a larger lens diameter 201 (right,FIG. 11B) compared to the smaller version (left, FIG. 11A). For example,a diameter between 1 mm and 30 mm could be used. Existing prior art thatputs imaging systems in a thin form factor uses small diameter lenses,because the focal length is small and using a large diameter lens wouldnot provide a benefit. The invention and embodiments disclosed hereinenable long focal lengths and enables larger diameter lenses to providebenefits, such as sharper images and greater light collection that canbe useful for low-light photography which can benefit from largerlenses.

In operation and use and as shown in FIG. 12 , image processing andextraction may be performed using techniques known to those of ordinaryskill in the art. In order to reconstruct the in-focus image from theraw distorted image that includes the out-of-focus components shown inFIG. 7 (A, B, D), the image processing method in FIG. 12 can be usedcreate a focused image. In one example, first the point spread functionof the imaging system is measured by imaging a small object far awayonto the sensor. The resulting image is composed of the tightly focusedobject plus the out-of-focus components caused by light that underwentthe undesired number of partial reflections. Using this point spreadfunction, the original image can be reconstructed using variousdisclosed approaches listed below.

Method 1: If the out of focus components are larger than the imagingsensor, then they form a substantially constant background level. Inthese cases, this method provides reconstructing the desired image byadjusting the dark level of the imaging system, either by imagepost-processing or in the hardware.

Method 2: In some cases, if the out-of-focus image is highly blurry thein-focus image can be reconstructed using high-pass filtering to rejectthe low-frequency background.

Method 3: Using the point-spread-function, the desired image can bereconstructed using deconvolution digital signal processing techniqueswhich are known to one skilled in the art of signal processing.

EXAMPLE

FIG. 13 compares the magnification achieved by a prototype of theexemplary device. The image on the left (FIG. 13(A)) is from an iPhone7, the image in the middle (FIG. 13(B)) is from iPhone 11pro with 2×optical magnification, and the image on the right (FIG. 13(C)) is froman exemplary device. In the exemplary device, L₁=4 mm, L₂=5 mm, and L₃=2mm as defined in FIG. 1 . A quantitative comparison of the magnificationachieved by each device was carried out by using a doctor's officeSnellen eye exam chart, as described next.

When used in a patient setting, the patient views a Snellen eye chartfrom a prescribed distance (e.g. from 20 feet) and attempts to read rowswith successively smaller text. Each row corresponds to a certain levelof visual acuity. If the bottommost row that the patient can read is the20/40 row, then that means that at a distance of 20 feet the patient canonly read letters that the average person can read even at 40 feet. Thus20/40 vision is worse (is lower acuity) than what is defined as averagevision. When a person has 20/20 vision that means this person can seeclearly at a distance of 20 feet what should, on average, be seen atthat distance. 20/15 vision means that the bottommost row that thepatient can read when at a distance of 20 feet from the chart is the20/15 row, and this row corresponds to letters that an average personwould have to stand closer, to within 15 feet from the chart, to read.Thus 20/15 vision corresponds to visual acuity that is better than whatis defined as average vision.

In the context of cameras, the Snellen chart can be used toquantitatively measure camera magnification and resolution. The lowestrow that was readable in each photograph indicated the visual acuity(magnification and resolution) that was achieved by that device. Allphotographs of the Snellen chart were taken at the same distance fromthe chart. Snellen chart readings directly correspond to the smallestangle that can be distinguished by the visual system (eye or camera) andso directly represent magnification and resolution.

FIG. 13 (A) shows that an iPhone 7 achieved a visual acuity of 20/33(the bottommost line that could be clearly read in a photograph taken bythe iPhone 7 was the 20/33 line) and this 20/33 vision corresponds tovisual acuity (magnification and resolution) that is worse than 20/20vision. FIG. 13 (B), for photographs taken by the iPhone 11 pro with 2Xoptical magnification, the bottommost row that could be clearly read inthe photograph was the 20/16 row, and this 20/16 vision is slightlybetter (1.25× better) than 20/20 vision. FIG. 13 (C), for photographstaken by our exemplary prototype, the bottommost row that could beclearly read in the photographs was the 20/8 row, and this 20/8 issignificantly better than 20/20 vision (2.5×better). The magnificationof our exemplary prototype was 4.125× better than the iPhone 7 cameraand 2×better than the iPhone 11 camera (33/8=4.125× and 16/8=2×). Thisvisual acuity directly translates to being able to see more imagedetail, specifically to identify smaller features in the image, which isprecisely the benefit provided by a higher magnification system.

The methods described herein may be implemented in software, hardware,or a combination thereof, in different embodiments. In addition, theorder of the blocks of the methods may be changed, and various elementsmay be added, reordered, combined, omitted, modified, etc. Variousmodifications and changes may be made as would be obvious to a personskilled in the art having the benefit of this disclosure. The variousembodiments described herein are meant to be illustrative and notlimiting. Many variations, modifications, additions, and improvementsare possible. Accordingly, plural instances may be provided forcomponents described herein as a single instance. Boundaries betweenvarious components, operations and data stores are somewhat arbitrary,and particular operations are illustrated in the context of specificillustrative configurations. Other allocations of functionality areenvisioned and may fall within the scope of claims that follow. Finally,structures and functionality presented as discrete components in theexample configurations may be implemented as a combined structure orcomponent. These and other variations, modifications, additions, andimprovements may fall within the scope of embodiments as defined in theclaims that follow.

What is claimed is:
 1. An imaging system comprising: a lens having afocal length and configured to transmit light; a first partialreflector; a second partial reflector, wherein the transmitted lightundergoes one or multiple round-trip reflections between the firstpartial reflector and the second partial reflector; a time-integratingsensor configured to capture a raw image corresponding to focused andunfocused light exiting the second partial reflector; a signalprocessing unit configured reconstruct an in-focused image from the rawimage; an additional lens placed between the first partial reflector andthe second partial reflector; the lens, the first partial reflector, thesecond partial reflector; and the time-integrating sensor are alignedsubstantially along an optical axis, a distance between the lens and thetime-integrating sensor is less than the focal length.
 2. The imagingsystem of claim 1, wherein the imaging system has a thickness includingthe lens, the first partial reflector, the second partial reflector andthe time-integrating sensor, of less than 30 mm.
 3. The imaging systemof claim 2, wherein the lens has a diameter and the diameter is largerthan the thickness of the imaging system.
 4. The imaging system of claim1, wherein the time-integrating sensor is a Charge Coupled Device (CCD)or a Complementary Metal Oxide Semiconductor (CMOS) array.
 5. Theimaging system of claim 1, wherein the lens, the first partialreflector, the second partial reflector, and the time-integrating sensorare enclosed within a mobile device.
 6. The imaging system of claim 1,wherein the lens, the first partial reflector, and the second partialreflector are arranged to produce the focused light when the transmittedlight undergoes a desired number of round-trips reflections between thefirst partial reflector and the second partial reflector.
 7. A method toproduce an in-focused image of an object using a mobile device,comprising: transmitting light through a lens having a focal length;acquiring, using a sensor, a raw image corresponding to a sum of focusedand unfocused light resulting from one or more round-trip partialreflections of the transmitted light occurring between two or morepartial reflectors that are aligned substantially along a common opticalaxis; and reconstructing the in-focus image-from the raw image, whereinthe reconstruction of the in-focus image is done by digital signalprocessing.
 8. The method of claim 7, further comprising displaying thein-focused image on a screen-of the mobile device.
 9. The method ofclaim 7, wherein the reconstructing the in-focus image-comprisesprocessing the raw image using a background subtraction, high-passfiltering, or deconvolution algorithm.
 10. The method of claim 7,wherein a distance between the lens and the sensor is less than thefocal length.
 11. The method of claim 8, wherein the mobile device has athickness including the lens, the two or more partial reflectors and thesensor, of less than 30 mm.
 12. The method of claim 7, wherein thesensor is a time-integrating sensor.
 13. The method of claim 12, whereinthe time-integrating sensor is a Charge Coupled Device (CCD) orComplementary Metal Oxide Semiconductor (CMOS) array.
 14. The method ofclaim 12, wherein the lens and the two or more partial reflectors arearranged to produce-the focused light when the transmitted lightundergoes a desired number of round-trips reflections between-the two ormore partial reflectors.
 15. A mobile device comprising: a lens having afocal length and configured to transmit light; a first partialreflector, a second partial reflector, wherein the transmitted lightundergoes one or multiple round-trip reflections between the firstpartial reflector and the second partial reflector; a time-integratingsensor configured to capture a raw image corresponding to focused andunfocused light exiting the second partial reflector; and a signalprocessing unit configured to-reconstruct an in-focus image from the rawimage; wherein the reconstruction of the in-focus image is done bydigital signal processing, wherein a distance between the lens and thetime-integrating sensor is less than the focal length, and the lens, thefirst partial reflector, the second partial reflector, and thetime-integrating sensor are enclosed within the mobile device.
 16. Thedevice of claim 15, wherein the mobile device has a thickness includingthe lens, the first partial reflector, the second partial reflector andthe time-integrating sensor, of less than 30 mm.
 17. The device of claim15, wherein the time-integrating sensor is a Charge Coupled Device (CCD)or Complementary Metal Oxide Semiconductor (CMOS) array.
 18. The imagingsystem in claim 15, further comprising additional lenses placed betweenthe first partial reflector and the second partial reflector.